Exact solution and finite size properties of the $U_{q}[osp(2|2m)]$ vertex model

TL;DR

This paper solves the $U_{q}[osp(2|2m)]$ vertex model exactly using algebraic Bethe ansatz, analyzing its finite size and thermodynamic properties, revealing critical behavior and conformal anomalies depending on parameters.

Contribution

It provides an exact diagonalization of the transfer matrix for the $U_{q}[osp(2|2m)]$ vertex model and explores its finite size and critical properties across different regimes.

Findings

For m=1, a critical line with central charge c=-1 is identified.

Finite size corrections depend on the anisotropy, indicating multicritical behavior.

The spectrum's leading finite size behavior is conjectured for arbitrary m.

Abstract

We have diagonalized the transfer matrix of the $U_{q}[osp(2|2m)]$ vertex model by means of the algebraic Bethe ansatz method for a variety of grading possibilities. This allowed us to investigate the thermodynamic limit as well as the finite size properties of the corresponding spin chain in the massless regime. The leading behaviour of the finite size corrections to the spectrum is conjectured for arbitrary $m$. For $m=1$ we find a critical line with central charge $c=-1$ whose exponents vary continuously with the $q$-deformation parameter. For $m\geq 2$ the finite size term related to the conformal anomaly depends on the anisotropy which indicates a multicritical behaviour typical of loop models.